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Nordic
1990 Nordic
2
2
Part of
1990 Nordic
Problems
(1)
sqrt[3]{Σa_i^3} \le \sqrt{Σ_i^2}
Source: Nordic Mathematical Contest 1990 #2
10/5/2017
Let
a
1
,
a
2
,
.
.
.
,
a
n
a_1, a_2, . . . , a_n
a
1
,
a
2
,
...
,
a
n
be real numbers. Prove
a
1
3
+
a
2
3
+
.
.
.
+
a
n
3
3
≤
a
1
2
+
a
2
2
+
.
.
.
+
a
n
2
\sqrt[3]{a_1^3+ a_2^3+ . . . + a_n^3} \le \sqrt{a_1^2+ a_2^2+ . . . + a_n^2}
3
a
1
3
+
a
2
3
+
...
+
a
n
3
≤
a
1
2
+
a
2
2
+
...
+
a
n
2
(1) When does equality hold in (1)?
inequalities
powers